A comparison of three heuristic optimization algorithms for solving the multi-objective land allocation (MOLA) problem

Multi-objective land allocation (MOLA) can be regarded as a spatial optimization problem that allocates appropriate use to specific land units concerning some objectives and constraints. Simulating annealing (SA), genetic algorithm (GA), and particle swarm optimization (PSO) have been popularly applied to solve MOLA problems, but their performance has not been well evaluated. This paper applies the three algorithms to a common MOLA problem that aims to maximize land suitability and spatial compactness and minimize land conversion cost subject to the number of units allocated for each use. Their performance has been evaluated based on the solution quality and the computational cost. The results demonstrate that: (1) GA consistently achieves quality solutions that satisfy both the objectives and the constraints and the computational cost is lower. (2) The popular penalty function method does not work well for SA in handling the constraints. (3) The solution quality of PSO needs to be improved. Techniques that better adapt PSO for discrete variables in MOLA problems need to be developed. (4) All three algorithms take high computational costs to achieve quality solutions in handling the objective of maximizing spatial compactness. How to encourage compact allocation is a common problem for them.